Question

a spring mass system is hanging from the ceiling of an elevator in equilibrium .the elevator start accelerating upwords with acceleration.find- frequency and the amplitude of the resulting SHM​

Answer 1

When a spring mass system is arranged in a accelerating lift. Its frequency will not be effected by this motion, but its amplitude will be effected. To understand this, please refer the following explanation.

So, we know the angular of spring mass pendulum is,

ω = Km

Here, untill and unless, we change either mass or spring, frequency (angular and also linear) is not going to be effected.

If the lift starts suddenly accelerating upwards, then the point of equilibrium for the oscillations of mass will be shifted from X0 to X1. Where, these two lengths will be as below.

When lift is not accelerating,

mg = KX0 ⇒ X0 = mgK

When lift is accelerating up with acceleration "a",

KX1 = mgeff ⇒ X1 = mgeffK⇒X1 = mg+aK

Therefore, the amplitude of the SHM changes from X0 to X1.

Hope this information will clear your doubts about the topic.